A049143 Revert transform of (1 - x - 2x^2 + x^3)/(1 - 2x^2 - 2x^3).

1, 1, 2, 4, 10, 26, 74, 219, 678, 2160, 7062, 23538, 79734, 273600, 948972, 3320845, 11708586, 41546434, 148236556, 531446460, 1913357426, 6914471176, 25071324984, 91181690872, 332528253078, 1215726924628, 4454924130364

Offset

1,3

Links

Table of n, a(n) for n=1..27.

Index entries for reversions of series

Formula

Recurrence: 49*(n-2)*(n-1)*n*(97276*n^6 - 3519516*n^5 + 45262750*n^4 - 283087617*n^3 + 934282738*n^2 - 1565876781*n + 1049863590)*a(n) = 84*(n-2)*(n-1)*(486380*n^7 - 18327150*n^6 + 254696367*n^5 - 1787076536*n^4 + 6991040383*n^3 - 15389861356*n^2 + 17672202225*n - 8109850050)*a(n-1) - 4*(n-2)*(23248964*n^8 - 934160180*n^7 + 14502686552*n^6 - 118351496900*n^5 + 565654855814*n^4 - 1636464877427*n^3 + 2810153593872*n^2 - 2619584037495*n + 1011295019700)*a(n-2) - 24*(1848244*n^9 - 80732634*n^8 + 1378035588*n^7 - 12765766611*n^6 + 72567277011*n^5 - 265962956799*n^4 + 632363275766*n^3 - 941709660585*n^2 + 794450752020*n - 286833522600)*a(n-3) + 16*(n-5)*(19455200*n^8 - 781724000*n^7 + 12160165721*n^6 - 99912786215*n^5 + 483488214059*n^4 - 1424023846157*n^3 + 2502350256972*n^2 - 2398791565710*n + 957442789080)*a(n-4) - 16*(n-6)*(n-5)*(11478568*n^7 - 409563604*n^6 + 5343328576*n^5 - 35012860513*n^4 + 127513525792*n^3 - 261159955705*n^2 + 280029420936*n - 121311223200)*a(n-5) + 304*(n-7)*(n-6)*(n-5)*(97276*n^6 - 2935860*n^5 + 29124310*n^4 - 135286257*n^3 + 322860367*n^2 - 382537080*n + 177022440)*a(n-6). - Vaclav Kotesovec, Jan 02 2021

Mathematica

Rest[CoefficientList[InverseSeries[Series[x*(1 - x - 2x^2 + x^3)/(1 - 2x^2 - 2x^3), {x, 0, 40}], x], x]] (* Vaclav Kotesovec, Jan 02 2021 *)

Crossrefs

Sequence in context: A351642 A206464 A089429 * A089404 A006123 A006251

Adjacent sequences: A049140 A049141 A049142 * A049144 A049145 A049146

Keyword

nonn

Author

Olivier Gérard

Status

approved