The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A289787 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A289787

p-INVERT of the even positive integers (A005843), where p(S) = 1 - S - S^2.
(history; published version)

#19 by Jon E. Schoenfield at Sat Aug 19 13:30:56 EDT 2017

STATUS

editing

approved

#18 by Jon E. Schoenfield at Sat Aug 19 13:30:54 EDT 2017

COMMENTS

Suppose s = (c(0), c(1), c(2), ...) is a sequence and p(S) is a polynomial. Let S(x) = c(0)*x + c(1)*x^2 + c(2)*x^3 + ... and T(x) = (-p(0) + 1/p(S(x)))/x. The p-INVERT of s is the sequence t(s) of coefficients in the Maclaurin series for T(x). Taking p(S) = 1 - S gives the INVERT transform of s, so that p-INVERT is a generalization of the INVERT transform (e.g., A033453).

STATUS

approved

editing

#17 by Alois P. Heinz at Mon Aug 14 19:34:48 EDT 2017

STATUS

proposed

approved

#16 by Clark Kimberling at Mon Aug 14 17:19:17 EDT 2017

STATUS

editing

proposed

#15 by Clark Kimberling at Mon Aug 14 17:06:47 EDT 2017

COMMENTS

Suppose s = (c(0), c(1), c(2), ...) is a sequence and p(S) is a polynomial. Let S(x) = c(0) *x + c(1)*x ^2 + c(2)*x^2 3 + ... and T(x) = (-p(0) + 1/p(S(x)))/x. The p-INVERT of s is the sequence t(s) of coefficients in the Maclaurin series for T(x). Taking p(S) = 1 - S gives the INVERT transform of s, so that p-INVERT is a generalization of the INVERT transform (e.g., A033453).

STATUS

approved

editing

#14 by OEIS Server at Fri Aug 11 18:34:34 EDT 2017

LINKS

Clark Kimberling, <a href="/A289787/b289787_1.txt">Table of n, a(n) for n = 0..1000</a>

#13 by Alois P. Heinz at Fri Aug 11 18:34:34 EDT 2017

STATUS

proposed

approved

Discussion

Fri Aug 11

18:34

OEIS Server: Installed new b-file as b289787.txt.  Old b-file is now b289787_1.txt.

#12 by Jon E. Schoenfield at Fri Aug 11 18:12:40 EDT 2017

STATUS

editing

proposed

#11 by Jon E. Schoenfield at Fri Aug 11 18:12:33 EDT 2017

CROSSREFS

Cf. A005843, A289788, A289780, A289788.

#10 by Jon E. Schoenfield at Fri Aug 11 18:12:09 EDT 2017

COMMENTS

Suppose s = (c(0), c(1), c(2), ...) is a sequence and p(S) is a polynomial. Let S(x) = c(0) + c(1)*x + c(2)*x^2 + ... and T(x) = (-p(0) + 1/p(S(x)))/x. The p-INVERT of s is the sequence t(s) of coefficients in the Maclaurin series for T(x). Taking p(S) = 1 - S gives the INVERT transform of s, so that p-INVERT is a generalization of the INVERT transform (e.g., A033453).

STATUS

proposed

editing