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A054843 Number of sequences of consecutive nonnegative integers (including sequences of length 1) that sum to n. 3
2, 1, 3, 1, 2, 3, 2, 1, 3, 3, 2, 2, 2, 2, 5, 1, 2, 3, 2, 2, 5, 2, 2, 2, 3, 2, 4, 3, 2, 4, 2, 1, 4, 2, 4, 4, 2, 2, 4, 2, 2, 4, 2, 2, 7, 2, 2, 2, 3, 3, 4, 2, 2, 4, 5, 2, 4, 2, 2, 4, 2, 2, 6, 1, 4, 5, 2, 2, 4, 4, 2, 3, 2, 2, 6, 2, 4, 5, 2, 2, 5, 2, 2, 4, 4, 2, 4, 2, 2, 6, 5, 2, 4, 2, 4, 2, 2, 3, 6, 3, 2, 4, 2, 2, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Number of nonnegative integer solutions (x, y) to the equation (2*x + y)*(1 + y)/2 = n. - Gionata Neri, Nov 15 2015

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A001227(n) + A010054(n). G.f.: Sum_{k>0} x^(k*(k-1)/2)/(1-x^k). - Vladeta Jovovic, Aug 10 2004

EXAMPLE

a(1) = 2 because 1 = 0+1 or 1; a(15) = 5 because 15 = 0+1+2+3+4+5 or 1+2+3+4+5 or 4+5+6 or 7+8 or 15.

MAPLE

N:= 1000:

G:= add(x^(k*(k-1)/2)/(1-x^k), k=1..floor((1+sqrt(1+8*N))/2)):

S:= series(G, x, N+1):

seq(coeff(S, x, j), j=0..N); # Robert Israel, Nov 15 2015

PROG

(PARI) vector(100, n, local(A); if( n<0, 0, A = x*O(x^n); polcoeff( eta(x^2+A)^2/eta(x+A), n)) + numdiv(n>>valuation(n, 2))) \\ Altug Alkan, Nov 15 2015

CROSSREFS

Cf. A001227, A054844.

Sequence in context: A132662 A279782 A132589 * A277427 A231631 A280700

Adjacent sequences:  A054840 A054841 A054842 * A054844 A054845 A054846

KEYWORD

easy,nonn

AUTHOR

Henry Bottomley, Apr 13 2000

STATUS

approved

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Last modified November 13 01:32 EST 2018. Contains 317118 sequences. (Running on oeis4.)