The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A325546 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A325546

Number of compositions of n with weakly increasing differences.
(history; published version)

#18 by Alois P. Heinz at Wed Aug 28 10:23:56 EDT 2019

STATUS

reviewed

approved

#17 by Michel Marcus at Wed Aug 28 10:18:21 EDT 2019

STATUS

proposed

reviewed

#16 by Andrew Howroyd at Wed Aug 28 10:16:50 EDT 2019

STATUS

editing

proposed

#15 by Andrew Howroyd at Wed Aug 28 10:15:15 EDT 2019

PROG

(PARI) \\ Row sums of R(n) give A007294 (=splits breakdown by width).

#14 by Andrew Howroyd at Wed Aug 28 10:14:24 EDT 2019

PROG

(PARI) \\ Row sums of R(n) give A007294 (=splits by width).

CROSSREFS

Cf. A000079, A000740, A007294, A008965, A070211 (concave-down compositions), A173258, A175342, A240026, A325360, A325545, A325547, A325548, A325552, A325557.

#13 by Andrew Howroyd at Wed Aug 28 10:00:20 EDT 2019

LINKS

Andrew Howroyd, <a href="/A325546/b325546.txt">Table of n, a(n) for n = 0..1000</a>

PROG

(PARI)

R(n)={my(L=List(), v=vectorv(n, i, 1), w=1, t=1); while(v, listput(L, v); w++; t+=w; v=vectorv(n, i, sum(k=1, (i-w-1)\t + 1, v[i-w-(k-1)*t]))); Mat(L)}

seq(n)={my(M=R(n)); Vec(1 + sum(i=1, n, my(p=sum(w=1, min(#M, n\i), x^(w*i)*sum(j=1, n-i*w, x^j*M[j, w]))); x^i/(1 - x^i)*(1 + p + O(x*x^(n-i)))^2))} \\ Andrew Howroyd, Aug 28 2019

STATUS

approved

editing

#12 by Alois P. Heinz at Sat May 11 17:46:12 EDT 2019

STATUS

proposed

approved

#11 by Alois P. Heinz at Sat May 11 17:30:29 EDT 2019

STATUS

editing

proposed

#10 by Alois P. Heinz at Sat May 11 17:28:01 EDT 2019

DATA

1, 1, 2, 4, 7, 11, 19, 28, 41, 62, 87, 120, 170, 228, 303, 408, 534, 689, 899, 1145, 1449, 1842, 2306, 2863, 3571, 4398, 5386, 6610, 8039, 9716, 11775, 14157, 16938, 20293, 24166, 28643, 33995, 40134, 47199, 55540, 65088, 75994, 88776, 103328, 119886, 139126

KEYWORD

nonn,more,changed

EXTENSIONS

More terms from Alois P. Heinz, May 11 2019

#9 by Alois P. Heinz at Sat May 11 17:27:28 EDT 2019

STATUS

proposed

editing