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A176653 Triangle, read by rows, defined by T(n, m) = f(n-m)*f(n) - f(n-0)*f(0) + 1, where f(n) is 1 if n = 0 and Prime(n) otherwise. 2
1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 4, 3, 4, 1, 1, 4, 5, 5, 4, 1, 1, 10, 9, 13, 9, 10, 1, 1, 10, 17, 19, 19, 17, 10, 1, 1, 16, 21, 37, 31, 37, 21, 16, 1, 1, 16, 29, 43, 55, 55, 43, 29, 16, 1, 1, 18, 29, 57, 63, 93, 63, 57, 29, 18, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are: {1, 2, 4, 6, 13, 20, 53, 94, 181, 288, 429, ...}.

LINKS

G. C. Greubel, Rows n = 0..100 of triangle, flattened

FORMULA

T(n, m) = f(n-m)*f(n) - f(n-0)*f(0) + 1, where f(n) is 1 if n = 0 and Prime(n) otherwise.

EXAMPLE

Triangle begins as:

  1;

  1,  1;

  1,  2,  1;

  1,  2,  2,  1;

  1,  4,  3,  4,  1;

  1,  4,  5,  5,  4,  1;

  1, 10,  9, 13,  9, 10,  1;

  1, 10, 17, 19, 19, 17, 10,  1;

  1, 16, 21, 37, 31, 37, 21, 16,  1;

  1, 16, 29, 43, 55, 55, 43, 29, 16,  1;

  1, 18, 29, 57, 63, 93, 63, 57, 29, 18, 1;

MATHEMATICA

f[n_]:= If[n==0, 1, Prime[n]]; T[n_, m_] = f[n-m]*f[m] - f[n]*f[0] + 1; Table[T[n, m], {n, 0, 12}, {m, 0, n}]//Flatten (* modified by G. C. Greubel, May 07 2019 *)

PROG

(PARI)

{f(n) = if(n==0, 1, prime(n)};

{T(n, k) = f(n-k)*f(k) - f(k) + 1};

for(n=0, 12, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, May 07 2019

(MAGMA)

f:= func< n | n eq 0 select 1 else NthPrime(n) >;

[[f(n-k)*f(k) - f(n) + 1: k in [0..n]]: n in [0..12]]; // G. C. Greubel, May 07 2019

(Sage)

def f(n):

    if (n==0): return 1

    else: return nth_prime(n)

def T(n, k): return f(n-k)*f(k) - f(n) +1

[[T(n, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, May 07 2019

CROSSREFS

Cf. A146985

Sequence in context: A240656 A106476 A101566 * A174842 A156074 A051287

Adjacent sequences:  A176650 A176651 A176652 * A176654 A176655 A176656

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Apr 22 2010

EXTENSIONS

Edited by G. C. Greubel, May 07 2019

STATUS

approved

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Last modified November 11 15:51 EST 2019. Contains 329019 sequences. (Running on oeis4.)