A088207 -id:A088207 - cp's OEIS frontend

A194126 -1+A088207.

1, 6, 13, 23, 36, 51, 69, 89, 112, 138, 166, 197, 231, 267, 306, 347, 391, 438, 487, 539, 593, 650, 710, 772, 837, 905, 975, 1048, 1123, 1201, 1282, 1365, 1451, 1540, 1631, 1725, 1821, 1920, 2022, 2126, 2233, 2342, 2454, 2569, 2686, 2806, 2929

Offset: 1

Clark Kimberling, Aug 15 2011

nonn

A194077 is the natural fractal sequence of A194126.

Cf. A088207, A194077, A194100.

c[k_]:=-1+Sum[Floor[j+j*GoldenRatio],{j,1,k}];
c=Table[c[k],{k,1,40}]

a(n)=-1+sum(floor(j+j*r) : 1<=j<=n), where r=(1+sqrt(5))/2, the golden ratio.

A117647 a(2n) = A014445(n), a(2n+1) = A015448(n+1).

Original entry on oeis.org

0, 1, 2, 5, 8, 21, 34, 89, 144, 377, 610, 1597, 2584, 6765, 10946, 28657, 46368, 121393, 196418, 514229, 832040, 2178309, 3524578, 9227465, 14930352, 39088169, 63245986, 165580141, 267914296, 701408733, 1134903170, 2971215073, 4807526976, 12586269025, 20365011074, 53316291173

Offset: 0

Creighton Dement, Apr 10 2006

Because of g.f. in Formula section, numbers k + 1 such that A088207(k)/k is an integer. - Ctibor O. Zizka, Apr 07 2025

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,4,0,1).

Cf. A000045, A001950, A007494, A014445, A015448, A033887, A059973, A088207.

I:=[0,1,2,5]; [n le 4 select I[n] else 4*Self(n-2) +Self(n-4): n in [1..41]]; // G. C. Greubel, Jul 12 2021

Table[Fibonacci[(6*n+1 -(-1)^n)/4], {n, 0, 40}] (* G. C. Greubel, Jul 12 2021 *)

[fibonacci((6*n+1-(-1)^n)/4) for n in [0..40]] # G. C. Greubel, Jul 12 2021

a(n) = A059973(n+2) - A059973(n+1).
G.f.: x*(x+1)^2/(1 -4*x^2 -x^4).
a(n) = Fibonacci((6*n + 1 - (-1)^n)/4) = Fibonacci(A007494(n)). - G. C. Greubel, Jul 12 2021

cp's OEIS Frontend

A194126 -1+A088207.

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