A179906 - OEIS

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A179906

(1, 1, 2, 3, 5, 7, 11, ...) convolved with (1, 0, 1, 2, 3, 5, 7, 11, ...); given A000041 = (1, 1, 2, 3, 5, 7, ...).

1, 1, 3, 6, 12, 22, 40, 69, 117, 193, 312, 495, 773, 1189, 1804, 2706, 4011, 5888, 8558, 12335, 17627, 25007, 35212, 49263, 68470, 94618, 129990, 177661, 241548, 326862, 440229, 590366, 788321, 1048499, 1389097, 1833638, 2411752, 3161449, 4130448, 5379560, 6984883

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..40.

FORMULA

(1 + x + 3x^2 + 6x^3 + 12x^4 + ...) = (1 + x + 2x^2 + 3x^3 + 5x^4 + ...) *

(1 + x^2 + 2x^3 + 3x^4 + 5x^5 + ...); given A000041 = (1, 1, 2, 3, 5, 7, ...).

EXAMPLE

a(5) = 22 = (7, 5, 3, 2, 1, 1) dot (1, 0, 1, 2, 3, 5) = (7 + 0 + 3 + 4 + 3 + 5).

CROSSREFS

Cf. A000041.