A275112 Zero together with the partial sums of A064412.

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

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 *)
LinearRecurrence[{3, -2, -2, 4, -4, 2, 2, -3, 1}, {0, 1, 6, 20, 52, 112, 215, 375, 613}, 60] (* Harvey P. Dale, Jun 19 2022 *)

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