A053298 Partial sums of A027964.

1, 8, 34, 107, 281, 654, 1397, 2801, 5353, 9859, 17643, 30869, 53062, 89951, 150833, 250780, 414210, 680665, 1114160, 1818310, 2960806, 4813018, 7814074, 12674542, 20544191, 33283434, 53902532, 87272241, 141273663, 228658744

Offset: 0

Author

Barry E. Williams, Mar 04 2000

Keywords

• nonn
• easy

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-14,15,-5,-4,4,-1)

Crossrefs

Cf. A027964 and A000204.

A column in triangular array A027960.

Cf. A137176 (row k=5).

Programs

Magma

m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+2*x)/((1-x-x^2)*(1-x)^5))); // G. C. Greubel, May 24 2018

Mathematica

LinearRecurrence[{6,-14,15,-5,-4,4,-1},{1,8,34,107,281,654,1397},30] (* Harvey P. Dale, May 09 2018 *)
CoefficientList[Series[(1+2x)/((1-x-x^2)(1-x)^5), {x,0,50}], x] (* G. C. Greubel, May 24 2018 *)

PARI

x='x+O('x^30); Vec((1+2*x)/((1-x-x^2)*(1-x)^5)) \\ G. C. Greubel, May 24 2018

Formula

a(n) = 3*F(n+10) + F(n+9) - (3*n^4 + 58*n^3 + 489*n^2 + 2234*n + 4752)/24, where F(.) are the Fibonacci numbers (A000045).

a(n) = a(n-1) + a(n-2) + (3*n+4)*C(n+3, 3)/4.

G.f.: (1 + 2*x)/((1 - x - x^2)*(1 - x)^5). - R. J. Mathar, Nov 28 2008