A250121 Crystal ball sequence for planar net 3.3.3.3.6.

1, 6, 15, 30, 49, 73, 102, 135, 174, 217, 265, 318, 375, 438, 505, 577, 654, 735, 822, 913, 1009, 1110, 1215, 1326, 1441, 1561, 1686, 1815, 1950, 2089, 2233, 2382, 2535, 2694, 2857, 3025, 3198, 3375, 3558, 3745, 3937, 4134

Offset

0,2

Comments

The g.f. was proven; cf. the comment in A250120. - Georg Fischer, Jul 19 2020

Links

Table of n, a(n) for n=0..41.

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1).

Formula

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

Mathematica

CoefficientList[Series[(x^2+x+1)*(x^4+3*x^3+3*x+1)/((x^4+x^3+x^2+x+1)*(1-x)^3), {x, 0, 41}], x] (* Georg Fischer, Jul 19 2020 *)
LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {1, 6, 15, 30, 49, 73, 102}, 50] (* Harvey P. Dale, Apr 30 2022 *)

Crossrefs

Partial sums of A250120.

Sequence in context: A336905 A097889 A256874 * A024802 A331073 A011886

Adjacent sequences: A250118 A250119 A250120 * A250122 A250123 A250124

Keyword

nonn,easy

Author

Bradley Klee and N. J. A. Sloane, Nov 23 2014

Status

approved