A027963 T(n,n+3), T given by A027960.

1, 6, 19, 47, 101, 199, 370, 661, 1148, 1954, 3278, 5442, 8967, 14696, 23993, 39065, 63483, 103025, 167040, 270655, 438346, 709716, 1148844, 1859412, 3009181, 4869594, 7879855, 12750611, 20631713, 33383659, 54016798, 87401977, 141420392, 228824086, 370246298, 599072310, 969320643

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-5,1,2,-1).

Crossrefs

Cf. A000032.

Programs

GAP

List([3..40], n-> Lucas(1,-1,n+4)[2] - (3*n^2+5*n+14)/2 ) # G. C. Greubel, Jun 01 2019

Magma

[Lucas(n+4) -(3*n^2+5*n+14)/2: n in [3..40]]; // G. C. Greubel, Jun 01 2019

Mathematica

t[, 0] = 1; t[, 1] = 3; t[n_, k_] /; (k == 2*n) = 1; t[n_, k_] := t[n, k] = t[n-1, k-2] + t[n-1, k-1]; Table[t[n, n+3], {n, 3, 33}]  (* Jean-François Alcover, Dec 27 2013 *)
Table[LucasL[n+4] -(3*n^2+5*n+14)/2, {n,3,40}] (* G. C. Greubel, Jun 01 2019 *)

PARI

{a(n) = fibonacci(n+5) + fibonacci(n+3) - (3*n^2+5*n+14)/2}; \\ G. C. Greubel, Jun 01 2019

Sage

[lucas_number2(n+4,1,-1) - (3*n^2+5*n+14)/2 for n in (3..40)] # G. C. Greubel, Jun 01 2019

Formula

G.f.: x^3*(1+2*x)/((1-x)^3*(1-x-x^2)). Differences of A027964. - Ralf Stephan, Feb 07 2004

a(n) = Lucas(n+4) - (3*n^2 + 5*n + 14)/2.

Extensions

Terms a(34) onward added by G. C. Greubel, Jun 01 2019