This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A289802 p-INVERT of the quarter-squares (A002620), where p(S) = 1 - S - S^2. 2
 1, 4, 15, 53, 185, 643, 2234, 7764, 26988, 93819, 326149, 1133811, 3941521, 13702079, 47633109, 165588965, 575643853, 2001134880, 6956629199, 24183622175, 84070541130, 292257951771, 1015988587832, 3531923782817, 12278174929397, 42683134990390 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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). See A289780 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 (5, -5, -4, 12, -5, -4, 4, -1) FORMULA G.f.: (1 - x + 2 x^3 - x^4)/(1 - 5 x + 5 x^2 + 4 x^3 - 12 x^4 + 5 x^5 + 4 x^6 - 4 x^7 + x^8). a(n) = 5*a(n-1) - 5*a(n-2) - 4*a(n-3) + 12*a(n-4) - 5*a(n-5) - 4*a(n-6) + 4*a(n-7) - a(n-8). MATHEMATICA z = 60; s = x/((1 - x)^2*(1 - x^2)); p = 1 - s - s^2; Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A002620 *) Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A289802 *) CROSSREFS Cf. A002620, A289780. Sequence in context: A171309 A210781 A303271 * A071719 A289927 A164619 Adjacent sequences:  A289799 A289800 A289801 * A289803 A289804 A289805 KEYWORD nonn,easy AUTHOR Clark Kimberling, Aug 12 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 10 12:43 EST 2019. Contains 329896 sequences. (Running on oeis4.)