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A053298 Partial sums of A027964. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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)

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

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 *)

PROG

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

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

CROSSREFS

Cf. A027964 and A000204.

A column in triangular array A027960.

Cf. A137176 (row k=5).

Sequence in context: A066804 A033455 A172202 * A196311 A196284 A196334

Adjacent sequences:  A053295 A053296 A053297 * A053299 A053300 A053301

KEYWORD

nonn,easy

AUTHOR

Barry E. Williams, Mar 04 2000

STATUS

approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)