

A291183


pINVERT of the positive integers, where p(S) = 1  4*S + 2*S^2.


2



4, 22, 116, 608, 3180, 16618, 86812, 453440, 2368292, 12369174, 64601428, 337397536, 1762142540, 9203221994, 48066074172, 251036784256, 1311100720708, 6847542588950, 35762957380148, 186780746599392, 975507894703660, 5094827328491242, 26608975328086364
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OFFSET

0,1


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 pINVERT 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 pINVERT is a generalization of the "INVERT" transform (e.g., A033453).
See A290890 for a guide to related sequences.


LINKS

Clark Kimberling, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,16,8,1)


FORMULA

G.f.: (2 (2  5 x + 2 x^2))/(1  8 x + 16 x^2  8 x^3 + x^4).
a(n) = 8*a(n1)  16*a(n2) + 8*a(n3)  a(n4).


MATHEMATICA

z = 60; s = x/(1  x)^2; p = 1  4 s + 2 s^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A000027 *)
Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A291183 *)
LinearRecurrence[{8, 16, 8, 1}, {4, 22, 116, 608}, 40] (* Vincenzo Librandi, Aug 20 2017 *)


PROG

(Magma) I:=[4, 22, 116, 608]; [n le 4 select I[n] else 8*Self(n1)16*Self(n2)+8*Self(n3)Self(n4): n in [1..40]]; // Vincenzo Librandi, Aug 20 2017


CROSSREFS

Cf. A000027, A290890.
Sequence in context: A106835 A293966 A305554 * A245087 A155596 A244900
Adjacent sequences: A291180 A291181 A291182 * A291184 A291185 A291186


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Aug 19 2017


STATUS

approved



