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A305549 Crystal ball sequence for the lattice C_6. 2
1, 73, 985, 6321, 26577, 85305, 227305, 528865, 1110049, 2149033, 3898489, 6704017, 11024625, 17455257, 26751369, 39855553, 57926209, 82368265, 114865945, 157417585, 212372497, 282469881, 370879785, 481246113, 617731681, 785065321, 988591033, 1234319185 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A019562.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

R. Bacher, P. de la Harpe and B. Venkov, Séries de croissance et séries d'Ehrhart associées aux réseaux de racines, Annales de l'institut Fourier, Tome 49 (1999) no. 3 , p. 727-762.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

a(n) = (128*n^6 + 384*n^5 + 800*n^4 + 960*n^3 + 692*n^2 + 276*n + 45)/45.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7), for n>6.

a(n) = Sum_{k=0..6} binomial(12, 2k)*binomial(n+k, 6).

G.f.: (1 + 6*x + x^2)*(1 + 60*x + 134*x^2 + 60*x^3 + x^4) / (1 - x)^7. - Colin Barker, Jun 09 2018

PROG

(PARI) {a(n) = sum(k=0, 6, binomial(12, 2*k)*binomial(n+k, 6))}

(PARI) Vec((1 + 6*x + x^2)*(1 + 60*x + 134*x^2 + 60*x^3 + x^4) / (1 - x)^7 + O(x^40)) \\ Colin Barker, Jun 09 2018

CROSSREFS

Cf. A019562, A142992.

Sequence in context: A123811 A057522 A320205 * A320214 A008400 A090685

Adjacent sequences:  A305546 A305547 A305548 * A305550 A305551 A305552

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jun 09 2018

STATUS

approved

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Last modified July 26 16:44 EDT 2021. Contains 346294 sequences. (Running on oeis4.)