|
| |
|
|
A121470
|
|
Let M = [{0, 1}, {-1, 2}]; v[1] = {1, 7}; w[n] = {0, 3} if n is even, otherwise {0, 6}. Let v[n] = M.v[n - 1] + w[n]; then a(n) = v[n][[1]].
|
|
1
| |
|
|
1, 7, 16, 31, 49, 73, 100, 133, 169, 211, 256, 307, 361, 421, 484, 553, 625, 703, 784, 871, 961, 1057, 1156, 1261, 1369, 1483, 1600, 1723, 1849, 1981, 2116, 2257, 2401, 2551, 2704, 2863, 3025, 3193, 3364, 3541, 3721, 3907, 4096, 4291, 4489, 4693, 4900
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
FORMULA
| a(n)=2*a(n-1)-2*a(n-3)+a(n-4) = 5/8-3n/2+9n^2/4+3*(-1)^n/8. G.f.: x*(1+5*x+2*x^2+x^3)/((1+x)*(1-x)^3). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 10 2009]
|
|
|
MAPLE
| A121410 := proc(nmin) local M, a, v, wev, wod, n ; a := [] ; M := linalg[matrix](2, 2, [0, 1, -1, 2]) ; v := linalg[vector](2, [1, 7]) ; wev := linalg[vector](2, [0, 3]) ; wod := linalg[vector](2, [0, 6]) ; while nops(a) < nmin do a := [op(a), v[1]] ; n := nops(a)+1 ; v := evalm(M &* v) ; if n mod 2 = 0 then v := evalm(v+wev) ; else v := evalm(v+wod) ; fi ; od: RETURN(a) ; end: A121410(80) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 18 2007
|
|
|
MATHEMATICA
| M := {{0, 1}, {-1, 2} } v[1] = {1, 7} w[n_] = If[Mod[n, 2] == 0, {0, 3}, {0, 6}] v[n_] := v[n] = M.v[n - 1] + w[n] a = Table[v[n][[1]], {n, 1, 30}]
|
|
|
CROSSREFS
| Cf. A003215, A005448.
Sequence in context: A024627 A180724 A140511 * A019541 A190661 A176449
Adjacent sequences: A121467 A121468 A121469 * A121471 A121472 A121473
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 07 2006
|
|
|
EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 16 2006
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 18 2007
|
| |
|
|
