The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A017900 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A017900

Expansion of 1/(1 - x^6 - x^7 - x^8 - ...).
(history; published version)

#70 by Michel Marcus at Wed Feb 07 12:58:40 EST 2024

STATUS

reviewed

approved

#69 by Hugo Pfoertner at Wed Feb 07 12:51:51 EST 2024

STATUS

proposed

reviewed

#68 by Joerg Arndt at Wed Feb 07 00:48:57 EST 2024

STATUS

editing

proposed

#67 by Joerg Arndt at Wed Feb 07 00:48:14 EST 2024

NAME

Expansion of 1/(1 - x^6 - x^7 - x^8 - ...).

STATUS

proposed

editing

#66 by Jon E. Schoenfield at Tue Feb 06 18:52:56 EST 2024

STATUS

editing

proposed

#65 by Jon E. Schoenfield at Tue Feb 06 18:52:53 EST 2024

COMMENTS

Number of compositions of n into parts >= 6. - Milan Janjic, Jun 28 2010

FORMULA

For positive integers n and k such that k <= n <= 6*k, and 5 divides n-k, define c(n,k) = binomial(k,(n-k)/5), and c(n,k ) = 0, otherwise. Then, for n >= 1, a(n+6) = sum(c(n,k), Sum_{k=1..n} c(n,k). - Milan Janjic, Dec 09 2011

STATUS

proposed

editing

#64 by Michel Marcus at Tue Feb 06 14:30:40 EST 2024

STATUS

editing

proposed

#63 by Michel Marcus at Tue Feb 06 14:30:29 EST 2024

LINKS

I. M. Gessel, and Ji Li, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Gessel/gessel6.html">Compositions and Fibonacci identities</a>, J. Int. Seq. 16 (2013) 13.4.5.

<a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 1).

FORMULA

G.f.: 1/(1-sum(Sum_{k>=6,} x^k)).

STATUS

proposed

editing

#62 by Linas Vepstas at Tue Feb 06 14:28:35 EST 2024

STATUS

editing

proposed

#61 by Linas Vepstas at Tue Feb 06 14:27:19 EST 2024

COMMENTS

Same as sequence A005708 with 1, 0, 0, 0, 0, 0 prepended. - Linas Vepstas, Feb 06 2024

STATUS

approved

editing

Discussion

Tue Feb 06

14:28

Linas Vepstas: Same as sequence A005708