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

Comments

Needs a b-file (not based on any conjectures, of course). - N. J. A. Sloane, Dec 18 2015

Links

Table of n, a(n) for n=0..39.

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

Formula

Empirical: Sum_{k=0..n} [(1903/72) + (3/8)*(-1)^k +19*KroneckerDelta[k,0] - 8*KroneckerDelta[k,1] - 12*KroneckerDelta[k,2] + ((k+1)/12)*(187*k-273) - (32*sqrt(3)/27)*((13/2)*cos((4k+1)*Pi/6) + sin(2k*Pi/3)) - (3*sqrt(26)/2)*(-1)^n*cos(k*Pi/2 + arctan(1/5)) - (3/4)*i^k*(1+(-1)^k)*(k+2)].- G. C. Greubel, Dec 18 2015

Empirical 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

Crossrefs

Cf. A009927.

Sequence in context: A031074 A285482 A175109 * A051878 A092653 A067465

Adjacent sequences: A265035 A265036 A265037 * A265039 A265040 A265041

Keyword

nonn

Author

N. J. A. Sloane, Dec 15 2015

Status

approved