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

Author

G. C. Greubel, Jul 04 2016

Keywords

• nonn

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).

Crossrefs

Cf. A213816.

Programs

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]

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

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).