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A275112 Zero together with the partial sums of A064412. 1
0, 1, 6, 20, 52, 112, 215, 375, 613, 948, 1407, 2013, 2799, 3793, 5034, 6554, 8398, 10603, 13220, 16290, 19870, 24006, 28761, 34185, 40347, 47302, 55125, 63875, 73633, 84463, 96452, 109668, 124204, 140133, 157554, 176544, 197208, 219628, 243915, 270155, 298465, 328936, 361691, 396825, 434467, 474717, 517710, 563550, 612378, 664303, 719472 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Luce ETIENNE, Illustration of initial terms of this sequence and A064412

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,4,-4,2,2,-3,1).

FORMULA

a(n) = (28*n^4+36*n^3+18*n^2+12*n+(1-(-1)^n))/16 for n even.

a(n) = (28*n^4+92*n^3+114*n^2+68*n+17-(-1)^n)/16 for n odd.

a(n) = (14*n^4+36*n^3+36*n^2+42*n+11+3*(2*n-1)*(-1)^n-8*(-1)^(((2*n-1+(-1)^n))/4))/128.

G.f.: x*(1+x+x^2)*(1+2*x+x^2+3*x^3) / ((1-x)^5*(1+x)^2*(1+x^2)). - Colin Barker, Jul 18 2016

MATHEMATICA

{0}~Join~Accumulate@ CoefficientList[Series[(1 + x + x^2) (1 + 2 x + x^2 + 3 x^3)/((1 - x)^2 (1 - x^2) (1 - x^4)), {x, 0, 49}], x] (* Michael De Vlieger, Jul 18 2016, after Wesley Ivan Hurt at A064412, or *)

Table[(14 n^4 + 36 n^3 + 36 n^2 + 42 n + 11 + 3 (2 n - 1) (-1)^n - 8 (-1)^(((2 n - 1 + (-1)^n))/4))/128, {n, 50}] (* Michael De Vlieger, Jul 18 2016 *)

PROG

(PARI) concat(0, Vec(x*(1+x+x^2)*(1+2*x+x^2+3*x^3)/((1-x)^5*(1+x)^2*(1+x^2)) + O(x^50))) \\ Colin Barker, Jul 18 2016

CROSSREFS

Cf. A064412, A213389, A006003.

Sequence in context: A119365 A001211 A122225 * A027178 A264314 A055909

Adjacent sequences:  A275109 A275110 A275111 * A275113 A275114 A275115

KEYWORD

nonn,easy

AUTHOR

Luce ETIENNE, Jul 17 2016

STATUS

approved

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Last modified February 17 12:32 EST 2020. Contains 331996 sequences. (Running on oeis4.)