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

Author

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

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

Partial sums of A250120.

Programs

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 *)

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).