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a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (natural numbers >= 3), t = (Lucas numbers).
(history; published version)

#9 by Harvey P. Dale at Mon Jan 23 16:27:01 EST 2017

STATUS

editing

approved

#8 by Harvey P. Dale at Mon Jan 23 16:26:57 EST 2017

MATHEMATICA

LinearRecurrence[{1, 3, -2, -1, -1, -3, 2, 1, 1, 1}, {9, 12, 37, 61, 133, 214, 413, 669, 1208, 1954}, 30] (* Harvey P. Dale, Jan 23 2017 *)

STATUS

approved

editing

#7 by Charles R Greathouse IV at Sat Jun 13 00:49:05 EDT 2015

LINKS

<a href="/index/Rec#order_10">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (1,3,-2,-1,-1,-3,2,1,1,1).

Discussion

Sat Jun 13

00:49

OEIS Server: https://oeis.org/edit/global/2439

#6 by R. J. Mathar at Wed Sep 25 05:06:55 EDT 2013

STATUS

editing

approved

#5 by R. J. Mathar at Wed Sep 25 05:06:48 EDT 2013

LINKS

<a href="/index/Rec#order_10">Index to sequences with linear recurrences with constant coefficients</a>, signature (1,3,-2,-1,-1,-3,2,1,1,1).

FORMULA

G.f.: x^2*(-9+4*x^7+2*x^6+7*x^5+6*x^4-6*x^3+2*x^2-3*x) /((x^2+x-1)*(x^4+x^2-1)^2) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009]

STATUS

approved

editing

#4 by Russ Cox at Fri Mar 30 18:56:00 EDT 2012

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu)

Clark Kimberling

Discussion

Fri Mar 30

18:56

OEIS Server: https://oeis.org/edit/global/285

#3 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

FORMULA

G.f.:(-9+4*x^7+2*x^6+7*x^5+6*x^4-6*x^3+2*x^2-3*x)/((x^2+x-1)*(x^4+x^2-1)^2) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009]

KEYWORD

nonn,new

nonn

#2 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

KEYWORD

nonn,new

nonn

AUTHOR

Clark Kimberling (ck6@cedar.(AT)evansville.edu)

#1 by N. J. A. Sloane at Sat Dec 11 03:00:00 EST 1999

NAME

a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (natural numbers >= 3), t = (Lucas numbers).

DATA

9, 12, 37, 61, 133, 214, 413, 669, 1208, 1954, 3394, 5492, 9309, 15062, 25131, 40663, 67147, 108646, 178181, 288303, 470670, 761560, 1239524, 2005592, 3257761, 5271168, 8550753

OFFSET

2,1

KEYWORD

nonn

AUTHOR

Clark Kimberling (ck6@cedar.evansville.edu)

STATUS

approved