A265038 Partial sums of A009927.

1, 13, 63, 183, 401, 745, 1291, 2019, 2921, 4133, 5659, 7443, 9597, 12149, 15103, 18535, 22389, 26729, 31727, 37231, 43233, 50001, 57443, 65467, 74281, 83853, 94187, 105419, 117397, 130221, 144159, 158927, 174517, 191329, 209175, 227927, 247889, 268969, 291171, 314691

Offset

0,2

Links

Jianing Song, Table of n, a(n) for n = 0..1000

V. A. Blatov, A. P. Shevchenko, and D. M. Proserpio, Applied Topological Analysis of Crystal Structures with the Program Package ToposPro, Cryst. Growth Des. 2014, 14, 3576-3586. See Table I.

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

Formula

G.f.: (1 +12*x +51*x^2 +130*x^3 +243*x^4 +350*x^5 +450*x^6 +418*x^7 +327*x^8 +182*x^9 +51*x^10 +16*x^11 -7*x^12 +8*x^13 +12*x^14) / ((1 -x)^4*(1 +x)*(1 +x^2)^2*(1 +x +x^2)^2). - Colin Barker, Dec 19 2015

From Jianing Song, May 22 2026: (Start)

a(n) = a(n-1) - a(n-2) + 3*a(n-3) - a(n-4) + a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8) - a(n-9) + 3*a(n-10) - a(n-11) + a(n-12) - a(n-13) for n >= 15.

a(n) = (374*n^3 + 303*n^2 + c1*n + c0)/72 for n >= 2, where c1 = [204,204,120,312,204,12,312,312,12,204,312,120] and c0 = [-1368,-809,92,-585,-728,-745,-612,55,-664,-1449,28,119] for n == 0..11 (mod 12). (End)

Prog

(PARI) a(n) = if(n<=1, [1, 13][n+1], my(c1=[204, 204, 120, 312, 204, 12, 312, 312, 12, 204, 312, 120], c0 = [-1368, -809, 92, -585, -728, -745, -612, 55, -664, -1449, 28, 119]); (374*n^3 + 303*n^2 + c1[n%12+1]*n + c0[n%12+1])/72) \\ Jianing Song, May 22 2026

Crossrefs

Cf. A009927.

Sequence in context: A031074 A285482 A175109 * A051878 A092653 A067465

Adjacent sequences: A265035 A265036 A265037 * A265039 A265040 A265041

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 15 2015

Status

approved