login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A172356 Triangle T(n, k) = round( c(n)/(c(k)*c(n-k)) ), where c(n) = Product_{j=1..n} A078012(j+3), read by rows. 1
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 3, 6, 6, 3, 1, 1, 4, 12, 24, 12, 4, 1, 1, 6, 24, 72, 72, 24, 6, 1, 1, 9, 54, 216, 324, 216, 54, 9, 1, 1, 13, 117, 702, 1404, 1404, 702, 117, 13, 1, 1, 19, 247, 2223, 6669, 8892, 6669, 2223, 247, 19, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,12

LINKS

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

FORMULA

T(n, k, q) = round( c(n,q)/(c(k,q)*c(n-k,q)) ), where c(n,q) = Product_{j=1..n} f(j,q), f(n,q) = q*f(n-1,q) + f(n-3,q), f(0,q) = 0, f(1,q) = f(2,q) = 1, and q = 1.

T(n, k) = round( c(n)/(c(k)*c(n-k)) ), where c(n) = Product_{j=1..n} A078012(j+3). - G. C. Greubel, May 09 2021

EXAMPLE

Triangle begins as:

  1;

  1,  1;

  1,  1,   1;

  1,  1,   1,    1;

  1,  2,   2,    2,    1;

  1,  3,   6,    6,    3,    1;

  1,  4,  12,   24,   12,    4,    1;

  1,  6,  24,   72,   72,   24,    6,    1;

  1,  9,  54,  216,  324,  216,   54,    9,   1;

  1, 13, 117,  702, 1404, 1404,  702,  117,  13,  1;

  1, 19, 247, 2223, 6669, 8892, 6669, 2223, 247, 19, 1;

MATHEMATICA

f[n_, q_]:= f[n, q]= If[n<3, Fibonacci[n], q*f[n-1, q] + f[n-3, q]];

c[n_, q_]:= Product[f[j, q], {j, n}];

T[n_, k_, q_]:= Round[c[n, q]/(c[k, q]*c[n-k, q])];

Table[T[n, k, 1], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, May 09 2021 *)

PROG

(Sage)

@CachedFunction

def f(n, q): return fibonacci(n) if (n<3) else q*f(n-1, q) + f(n-3, q)

def c(n, q): return product( f(j, q) for j in (1..n) )

def T(n, k, q): return round(c(n, q)/(c(k, q)*c(n-k, q)))

flatten([[T(n, k, 1) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 09 2021

CROSSREFS

cf. A078012.

Sequence in context: A128084 A131823 A089722 * A184948 A242775 A079562

Adjacent sequences:  A172353 A172354 A172355 * A172357 A172358 A172359

KEYWORD

nonn,tabl,less

AUTHOR

Roger L. Bagula, Feb 01 2010

EXTENSIONS

Definition corrected to give integral terms by G. C. Greubel, May 09 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 17 05:39 EDT 2021. Contains 345080 sequences. (Running on oeis4.)