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A285116 Triangle read by rows: T(0,n) = T(n,n) = 1; and for n > 0, 0 < k < n, T(n,k) = C(n-1,k-1) OR C(n-1,k), where C(n,k) is binomial coefficient (A007318) and OR is bitwise-OR (A003986). 4
1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 3, 3, 3, 1, 1, 5, 6, 6, 5, 1, 1, 5, 15, 10, 15, 5, 1, 1, 7, 15, 31, 31, 15, 7, 1, 1, 7, 23, 55, 35, 55, 23, 7, 1, 1, 9, 28, 60, 126, 126, 60, 28, 9, 1, 1, 9, 45, 116, 126, 126, 126, 116, 45, 9, 1, 1, 11, 47, 125, 250, 254, 254, 250, 125, 47, 11, 1, 1, 11, 63, 183, 495, 462, 462, 462, 495, 183, 63, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10439; the rows 0 - 143 of triangle

Index entries for triangles and arrays related to Pascal's triangle

FORMULA

T(0,n) = T(n,n) = 1; and for n > 0, 0 < k < n, T(n,k) = C(n-1,k-1) OR C(n-1,k), where C(n,k) is binomial coefficient (A007318) and OR is bitwise-OR (A003986).

T(n,k) = A285117(n,k) + A285118(n,k).

C(n,k) = T(n,k) + A285118(n,k). [Where C(n,k) = A007318.]

EXAMPLE

Rows 0 - 12 of the triangle:

  1,

  1, 1,

  1, 1, 1,

  1, 3, 3, 1,

  1, 3, 3, 3, 1,

  1, 5, 6, 6, 5, 1,

  1, 5, 15, 10, 15, 5, 1,

  1, 7, 15, 31, 31, 15, 7, 1,

  1, 7, 23, 55, 35, 55, 23, 7, 1,

  1, 9, 28, 60, 126, 126, 60, 28, 9, 1,

  1, 9, 45, 116, 126, 126, 126, 116, 45, 9, 1,

  1, 11, 47, 125, 250, 254, 254, 250, 125, 47, 11, 1,

  1, 11, 63, 183, 495, 462, 462, 462, 495, 183, 63, 11, 1

MATHEMATICA

T[n_, k_]:= If[n==0 || n==k, 1, BitOr[Binomial[n - 1, k - 1], Binomial[n - 1, k]]]; Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Indranil Ghosh, Apr 16 2017 *)

PROG

(Scheme)

(define (A285116 n) (A285116tr (A003056 n) (A002262 n)))

(define (A285116tr n k) (cond ((zero? k) 1) ((= k n) 1) (else (A003986tr (A007318tr (- n 1) (- k 1)) (A007318tr (- n 1) k))))) ;; Where A003986bi implements bitwise-OR (A003986) and A007318tr gives the binomial coefficients (A007318).

(PARI) T(n, k) = if (n==0 || n==k, 1, bitor(binomial(n - 1, k - 1), binomial(n - 1, k)));

for(n=0, 12, for(k=0, n, print1(T(n, k), ", "); ); print(); ) \\ Indranil Ghosh, Apr 16 2017

CROSSREFS

Cf. A003986, A007318, A285117, A285118.

Cf. A285113 (row sums).

Sequence in context: A084101 A053386 A301303 * A266529 A266509 A266539

Adjacent sequences:  A285113 A285114 A285115 * A285117 A285118 A285119

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Apr 16 2017

STATUS

approved

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Last modified July 13 04:31 EDT 2020. Contains 335673 sequences. (Running on oeis4.)