A274759 Modified quadranacci series.

0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 6, 7, 8, 12, 14, 15, 23, 27, 29, 44, 52, 56, 85, 100, 108, 164, 193, 208, 316, 372, 401, 609, 717, 773, 1174, 1382, 1490, 2263, 2664, 2872, 4362, 5135, 5536, 8408, 9898, 10671, 16207, 19079, 20569, 31240, 36776, 39648, 60217, 70888, 76424, 116072, 136641

Offset

0,6

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Ian Bruce, A Modified Tribonacci Sequence, The Fibonacci Quarterly 22, no.3 (1984):244-246

Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,0,1,0,0,1,0,0,1).

Formula

a(3n) = a(3n-3) + a(3n-6) + a(3n-9) + a(3n-12).

a(3n + 2) = a(3n + 1) + a(3n - 2).

a(3n + 3) = a(3n + 1) + a(3n - 1).

a(3n + 4) = a(3n + 1) + a(3n).

G.f.: x*(1 + x + x^2 + x^4 + x^5 + x^8)/(1 - x^3 - x^6 - x^9 - x^12).

Mathematica

CoefficientList[Series[x*(1 + x + x^2 + x^4 + x^5 + x^8)/(1 - x^3 - x^6 - x^9 - x^12), {x, 0, 25}], x] (* or *) LinearRecurrence[{0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1}, {0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 6}, 50]

Prog

(PARI) concat(0, Vec(x*(1+x+x^2+x^4+x^5+x^8)/(1-x^3-x^6-x^9-x^12) + O(x^99))) \\ Altug Alkan, Jul 04 2016

Crossrefs

Cf. A213816.

Sequence in context: A096938 A130084 A017981 * A274157 A005863 A015740

Adjacent sequences: A274756 A274757 A274758 * A274760 A274761 A274762

Keyword

nonn,changed

Author

G. C. Greubel, Jul 04 2016

Status

approved