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A117502 Triangle, row sums = A001595. 2
1, 1, 2, 1, 1, 3, 1, 1, 2, 5, 1, 1, 2, 3, 8, 1, 1, 2, 3, 5, 13, 1, 1, 2, 3, 5, 8, 21, 1, 1, 2, 3, 5, 8, 13, 34, 1, 1, 2, 3, 5, 8, 13, 21, 55, 1, 1, 2, 3, 5, 8, 13, 21, 34, 89, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 144, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 233 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row sums = A001595 = (1, 3, 9, 15, 25, 41, ...).

LINKS

G. C. Greubel, Rows n = 1..100 of triangle, flattened

FORMULA

n-th row = first n Fibonacci terms, with a deletion of F(n).

Columns of the triangle are difference terms of the array in A117501.

T(n,k) = Fibonacci(k) for k < n and T(n,n) = Fibonacci(n+1). - G. C. Greubel, Jul 10 2019

EXAMPLE

Row 5 of the triangle = (1, 1, 2, 3, 8); the first 5 Fibonacci terms with a deletion of F(5) = 5.

First few rows of the triangle are:

  1;

  1, 2;

  1, 1, 3;

  1, 1, 2, 5;

  1, 1, 2, 3, 8; ...

MATHEMATICA

Table[If[k==n, Fibonacci[n+1], Fibonacci[k]], {n, 20}, {k, n}]//Flatten (* G. C. Greubel, Jul 10 2019 *)

PROG

(PARI) T(n, k) = if(k==n, fibonacci(n+1), fibonacci(k)); \\ G. C. Greubel, Jul 10 2019

(MAGMA) [k eq n select Fibonacci(n+1) else Fibonacci(k): k in [1..n], n in [1..20]]; // G. C. Greubel, Jul 10 2019

(Sage)

def T(n, k):

    if (k==n): return fibonacci(n+1)

    else: return fibonacci(k)

[[T(n, k) for k in (1..n)] for n in (1..20)] # G. C. Greubel, Jul 10 2019

(GAP)

T:= function(n, k)

    if k=n then return Fibonacci(n+1);

    else return Fibonacci(k);

    fi;

  end;

Flat(List([1..20], n-> List([1..n], k-> T(n, k) ))); # G. C. Greubel, Jul 14 2019

CROSSREFS

Cf. A000045, A117501, A001595.

Sequence in context: A306680 A083312 A032435 * A212630 A030360 A232529

Adjacent sequences:  A117499 A117500 A117501 * A117503 A117504 A117505

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Mar 23 2006

EXTENSIONS

More terms added by G. C. Greubel, Jul 10 2019

STATUS

approved

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Last modified May 26 09:37 EDT 2020. Contains 334620 sequences. (Running on oeis4.)