A207539 -id:A207539 - cp's OEIS frontend

A163551 13th-order Fibonacci numbers: a(n) = a(n-1) + ... + a(n-13) with a(1)=...=a(13)=1.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 25, 49, 97, 193, 385, 769, 1537, 3073, 6145, 12289, 24577, 49153, 98305, 196597, 393169, 786289, 1572481, 3144769, 6289153, 12577537, 25153537, 50304001, 100601857, 201191425, 402358273, 804667393

Offset: 1

Jainit Purohit (mjainit(AT)gmail.com), Jul 30 2009

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Kai Wang, Identities for generalized enneanacci numbers, Generalized Fibonacci Sequences (2020).
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1,1,1,1,1,1,1).

Cf. A000045 (Fibonacci numbers), A000213 (tribonacci), A000288 (tetranacci), A000322 (pentanacci), A000383 (hexanacci), A060455 (heptanacci), A123526 (octanacci), A127193 (nonanacci), A127194 (decanacci), A127624 (undecanacci), A207539 (dodecanacci).

With[{c=Table[1,{13}]},LinearRecurrence[c,c,40]] (* Harvey P. Dale, Aug 09 2013 *)

x='x+O('x^50); Vec((1-x^2 -2*x^3-3*x^4 -4*x^5-5*x^6 -6*x^7-7*x^8 -8*x^9 -9*x^10 -10*x^11 -11*x^12) / (1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13)) \\ G. C. Greubel, Jul 28 2017

a(n) = a(n-1)+a(n-2)+...+a(n-13) for n > 12, a(0)=a(1)=...=a(12)=1.

G.f.: (-1)*(-1+x^2+2*x^3+3*x^4+4*x^5+5*x^6+6*x^7+7*x^8+8*x^9+9*x^10 +10*x^11 +11*x^12) / (1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13). - Michael Burkhart, Feb 18 2012

Values adapted to the definition by R. J. Mathar, Aug 01 2009

A249169 Fibonacci 16-step numbers, a(n) = a(n-1) + a(n-2) + ... + a(n-16).

Original entry on oeis.org

1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65535, 131069, 262136, 524268, 1048528, 2097040, 4194048, 8388032, 16775936, 33551616, 67102720, 134204416, 268406784, 536809472, 1073610752, 2147205120, 4294377472, 8588689409

Offset: 15

Alan N. Inglis, Oct 22 2014

M. Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, J. Int. Seq. 18 (2015) # 15.4.7.
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1).

Other k-step Fibonacci sequences: Cf. A000045, A000213, A000288, A000322, A000383, A060455, A123526, A127193, A127194, A168083, A207539, A168084, A220469, A220493.

a:= proc(n) option remember; `if`(n<15, 0,
      `if`(n=15, 1, add(a(n-j), j=1..16)))
    end:
seq(a(n), n=15..50);  # Alois P. Heinz, Oct 23 2014

CoefficientList[Series[-1 /(x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x - 1), {x, 0, 50}], x] (* Vincenzo Librandi, Nov 21 2014 *)

a(n) = a(n-1) + a(n-2) + ... + a(n-16).

G.f.: -x^15 / (x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5 +x^4+x^3+x^2+x-1). - Alois P. Heinz, Oct 23 2014

cp's OEIS Frontend

A163551 13th-order Fibonacci numbers: a(n) = a(n-1) + ... + a(n-13) with a(1)=...=a(13)=1.

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