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A072951 a(n) = sum(k>=2, z(k)*v(k)^n) where v(k) is the real positive solution to x^k=x+1 (i.e. the k-th Pisot-Vijayaraghavan number) and z(k) is the real positive root of a polynomial P(k,x) with integer coefficients of degree k. 2
1, 2, 4, 6, 11, 15, 27, 39, 63, 100, 159, 247, 403, 641, 1023, 1644, 2653, 4264, 6872, 11081, 17895, 28899, 46680, 75420, 121918, 197113, 318728, 515420, 833592, 1348309, 2181022, 3528144, 5707568, 9233629, 14938481, 24168531, 39102324 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In particular a(n) is asymptotic to (1/10)*(5+sqrt(5))*phi^n where phi is the golden ratio. First P(k,x) are P(2,x)=5x^2-5x-1; P(3,x)=23x^3-23x^2+8x-1; P(4)=283x^4-283x^3+105x^2-17x+1; P(5)=2869x^5-2869x^4+1154x^3-234x^2+24x -1.

a(n) is the number of compositions of n into almost equal parts. It means the difference between the largest part and the smallest part is at most 1. For example, there are 6 compositions of 4 into almost equal parts, (4), (2,2), (2,1,1), (1,2,1), (1,1,2), (1,1,1,1). - Ran Pan, Oct 16 2015

LINKS

Table of n, a(n) for n=1..37.

FORMULA

a(n) = Sum_{k=1, n} C(k, n mod k). - Benoit Cloitre, May 03 2003

PROG

(PARI) a(n)=sum(k=1, n, binomial(k, n%k))

CROSSREFS

Sequence in context: A187492 A103580 A094866 * A062766 A115269 A103692

Adjacent sequences:  A072948 A072949 A072950 * A072952 A072953 A072954

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Aug 20 2002

STATUS

approved

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Last modified June 28 04:43 EDT 2017. Contains 288813 sequences.