A299262 Partial sums of A299256.

1, 7, 25, 65, 137, 249, 411, 631, 919, 1283, 1733, 2277, 2925, 3685, 4567, 5579, 6731, 8031, 9489, 11113, 12913, 14897, 17075, 19455, 22047, 24859, 27901, 31181, 34709, 38493, 42543, 46867, 51475, 56375, 61577, 67089, 72921, 79081, 85579, 92423, 99623, 107187, 115125, 123445, 132157, 141269, 150791, 160731, 171099

Offset

0,2

Links

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

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

Formula

From Colin Barker, Feb 09 2018: (Start)

G.f.: (1 + 2*x)*(1 + 2*x + 2*x^2 + 2*x^3 - x^4) / ((1 - x)^4*(1 + x)).

a(n) = (6*n^3 + 9*n^2 + 2*n + 12) / 4 for n>0 and even.

a(n) = (6*n^3 + 9*n^2 + 2*n + 11) / 4 for n odd.

a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5) for n>5. (End)

E.g.f.: ((12 + 17*x + 27*x^2 + 6*x^3)*cosh(x) + (11 + 17*x + 27*x^2 + 6*x^3)*sinh(x) - 8)/4. - Stefano Spezia, Mar 14 2024

Mathematica

LinearRecurrence[{3, -2, -2, 3, -1}, {1, 7, 25, 65, 137, 249}, 50] (* Harvey P. Dale, Jul 22 2024 *)

Prog

(PARI) Vec((1 + 2*x)*(1 + 2*x + 2*x^2 + 2*x^3 - x^4) / ((1 - x)^4*(1 + x)) + O(x^60)) \\ Colin Barker, Feb 09 2018

Crossrefs

Cf. A299256.

The 28 uniform 3D tilings: cab: A299266, A299267; crs: A299268, A299269; fcu: A005901, A005902; fee: A299259, A299265; flu-e: A299272, A299273; fst: A299258, A299264; hal: A299274, A299275; hcp: A007899, A007202; hex: A005897, A005898; kag: A299256, A299262; lta: A008137, A299276; pcu: A005899, A001845; pcu-i: A299277, A299278; reo: A299279, A299280; reo-e: A299281, A299282; rho: A008137, A299276; sod: A005893, A005894; sve: A299255, A299261; svh: A299283, A299284; svj: A299254, A299260; svk: A010001, A063489; tca: A299285, A299286; tcd: A299287, A299288; tfs: A005899, A001845; tsi: A299289, A299290; ttw: A299257, A299263; ubt: A299291, A299292; bnn: A007899, A007202. See the Proserpio link in A299266 for overview.

Sequence in context: A155305 A155290 A056685 * A001296 A000970 A247620

Adjacent sequences: A299259 A299260 A299261 * A299263 A299264 A299265

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 07 2018

Status

approved