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A214604 revision #9

A214604

Odd numbers by transposing the right half of A176271, triangle read by rows: T(n,k) = A176271(n - 1 + k, n), 1 <= k <= n.

1, 5, 9, 11, 17, 25, 19, 27, 37, 49, 29, 39, 51, 65, 81, 41, 53, 67, 83, 101, 121, 55, 69, 85, 103, 123, 145, 169, 71, 87, 105, 125, 147, 171, 197, 225, 89, 107, 127, 149, 173, 199, 227, 257, 289, 109, 129, 151, 175, 201, 229, 259, 291, 325, 361, 131, 153

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Sums of rows: A214659; central terms: A214660;

T(n,1) = A028387(n-1); T(n,n) = A016754(n-1);

T(n,k) = A214661(n,k) + 2*A025581(n,k) = 2*A000290(A094727(n,k)) - A214661(n,k).

LINKS

Reinhard Zumkeller, Rows n = 1..150 of triangle, flattened

FORMULA

T(n,k) = (n+k)^2 - n - 3*k + 1.

EXAMPLE

. Take the first n elements of the n-th diagonal (northeast to

. southwest) of the triangle on the left side

. and write this as n-th row on the triangle of the right side.

. 1: 1 1

. 2: _ 5 5 9

. 3: _ 9 11 11 17 25

. 4: __ __ 17 19 19 27 37 49

. 5: __ __ 25 27 29 29 39 51 65 ..

. 6: __ __ __ 37 39 41 41 53 67 .. .. ..

. 7: __ __ __ 49 51 53 55 55 69 .. .. .. .. ..

. 8: __ __ __ __ 65 67 69 71 71 .. .. .. .. .. .. .. .

PROG

(Haskell)

import Data.List (transpose)

a214604 n k = a214604_tabl !! (n-1) !! (k-1)

a214604_row n = a214604_tabl !! (n-1)

a214604_tabl = zipWith take [1..] $ transpose a176271_tabl

CROSSREFS

Cf. A214661.

Sequence in context: A314601 A314602 A314603 * * A101284 A362156

Adjacent sequences: A214601 A214602 A214603 * A214605 A214606 A214607

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Jul 25 2012

STATUS

approved