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A174516 Partial sums of A002896. 1
1, 7, 97, 1957, 46687, 1219243, 33715399, 970085119, 28740443449, 870830918389, 26860099935529, 840549807424369, 26620996978712269, 851664885506669269, 27482469263443730269, 893460843597349019629, 29235859228655427097639 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of number of 2n-step polygons on cubic lattice. Equivalently, partial sums of number of walks with 2n steps on the cubic lattice Z x Z x Z beginning and ending at (0,0,0). The subsequence of primes in this partial sum begins: 7, 97, 46687.

LINKS

Table of n, a(n) for n=0..16.

FORMULA

a(n) = SUM[i=0..n] A002896(i) = SUM[i=0..n] C(2i, i) * A002893(i) = SUM[i=0..n] C(2i, i)*SUM[k=0..i] C(n, k)^2 * C(2k, k).

G.f.: g/(1-x) where g is the ogf of A002896. - Mark van Hoeij, Nov 12 2011

EXAMPLE

a(4) = 1 + 6 + 90 + 1860 + 44730 = 46687 is prime.

MAPLE

keyword = walk

MATHEMATICA

b[n_] := b[n] = (* A002896 *) Binomial[2*n, n]*HypergeometricPFQ[{1/2, -n, -n}, {1, 1}, 4]; a[n_] := Sum[b[k], {k, 0, n}]; Table[a[n], {n, 0, 16}] (* Jean-Fran├žois Alcover, Dec 20 2011 *)

CROSSREFS

Cf. A002896, A049020, A049037, A084261, A138540, A140476.

Sequence in context: A178808 A083083 A022007 * A058805 A305137 A132061

Adjacent sequences:  A174513 A174514 A174515 * A174517 A174518 A174519

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Mar 20 2010

STATUS

approved

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Last modified July 11 17:24 EDT 2020. Contains 335626 sequences. (Running on oeis4.)