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A053311 Partial sums of A000285. 3
1, 5, 10, 19, 33, 56, 93, 153, 250, 407, 661, 1072, 1737, 2813, 4554, 7371, 11929, 19304, 31237, 50545, 81786, 132335, 214125, 346464, 560593, 907061, 1467658, 2374723, 3842385, 6217112, 10059501, 16276617, 26336122 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 224.

LINKS

Table of n, a(n) for n=0..32.

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

FORMULA

a(n) = 4F(n+1) + F(n) - 4, where F(k) is the (k+1)st Fibonacci number(A000045).

From R. J. Mathar, Apr 29 2013: (Start)

G.f. ( 1+3*x ) / ( (x-1)*(x^2+x-1) ).

a(n) = A000071(n+3) + 3*A000071(n+2) = A000285(n+2) - 4. (End)

EXAMPLE

a(n) = a(n-1) + a(n-2) + 4; a(0)=1; n >= 1.

MATHEMATICA

a=0; b=1; lst={a, b}; Do[z=a+b+4; AppendTo[lst, z]; a=b; b=z, {n, 50}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 16 2010 *)

CROSSREFS

Cf. A000285.

a(n) = A101220(4, 1, n+1).

Sequence in context: A191595 A047882 A184260 * A147390 A115825 A115774

Adjacent sequences:  A053308 A053309 A053310 * A053312 A053313 A053314

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Mar 06 2000

STATUS

approved

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Last modified February 20 11:01 EST 2018. Contains 299385 sequences. (Running on oeis4.)