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

3,2

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).

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.

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 *)

Prog

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

Crossrefs

Cf. A000032.

Sequence in context: A070893 A272047 A267829 * A034199 A272752 A272803

Adjacent sequences: A027960 A027961 A027962 * A027964 A027965 A027966

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved