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A102713 Total sum of odd parts in all compositions of n. 2
1, 2, 8, 18, 48, 110, 260, 586, 1320, 2918, 6412, 13954, 30192, 64926, 138964, 296122, 628664, 1330134, 2805916, 5903090, 12388736, 25942542, 54215268, 113090858, 235502408, 489646150, 1016575020, 2107715426, 4364561680, 9027384958, 18651293172, 38495632794 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,3,-4,-4).

FORMULA

a(n) = ((15*n+4)*2^(n-1)-2*(3*n+1)*(-1)^n)/27.

From Colin Barker, Jan 08 2020: (Start)

G.f.: x*(1 + x^2) / ((1 + x)^2*(1 - 2*x)^2).

a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 4*a(n-4) for n>4.

(End)

PROG

(PARI) a(n)={((15*n+4)*2^(n-1) - 2*(3*n+1)*(-1)^n)/27} \\ Andrew Howroyd, Jan 08 2020

(PARI) Vec(x*(1 + x^2) / ((1 + x)^2*(1 - 2*x)^2) + O(x^35)) \\ Colin Barker, Jan 08 2020

CROSSREFS

Cf. A066967, A073371.

Sequence in context: A064009 A246148 A201348 * A332217 A249763 A114723

Adjacent sequences:  A102710 A102711 A102712 * A102714 A102715 A102716

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Feb 06 2005

EXTENSIONS

Terms a(26) and beyond from Andrew Howroyd, Jan 08 2020

STATUS

approved

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Last modified September 18 00:40 EDT 2021. Contains 347493 sequences. (Running on oeis4.)