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A101492 Triangle read by rows: T(n,k) = (n-k+1)*(4*k+1). 2
1, 2, 5, 3, 10, 9, 4, 15, 18, 13, 5, 20, 27, 26, 17, 6, 25, 36, 39, 34, 21, 7, 30, 45, 52, 51, 42, 25, 8, 35, 54, 65, 68, 63, 50, 29, 9, 40, 63, 78, 85, 84, 75, 58, 33, 10, 45, 72, 91, 102, 105, 100, 87, 66, 37, 11, 50, 81, 104, 119, 126, 125, 116, 99, 74, 41, 12, 55, 90, 117 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The triangle is generated from the product A*B

of the infinite lower triangular matrices A =

1 0 0 0...

1 1 0 0...

1 1 1 0...

1 1 1 1...

... and B =

1 0 0 0...

1 5 0 0...

1 5 9 0...

1 5 9 13...

...

T(n+0,0) = 1*n = A000027(n+1),

T(n+0,1) = 5*n = A008587(n),

T(n+1,2) = 9*n = A008591(n),

T(n+2,3) = 13*n = A008595(n),

so, for example,

T(n,n) = 4*n+1 = A016813(n),

T(n+1,n) = 8*n+2 = A017089(n),

T(n,0)*T(n,1)/10 = A000217(n) (triangular numbers),

T(n,n)*T(n,0) = A001107(n+1) (10-gonal numbers: 4*n^2 - 3*n),

T(n,n)*T(n,1)/5 = A007742(n).

LINKS

Muniru A Asiru, Rows n=0..150 of triangle, flattened

MATHEMATICA

Flatten[Table[(n+1-k)(4k+1), {n, 0, 15}, {k, 0, n}]] (* Harvey P. Dale, Jun 09 2011 *)

PROG

(PARI) T(n, k) = if(k>n, 0, (n-k+1)*(4*k+1));

for(i=0, 10, for(j=0, i, print1(T(i, j), ", ")); print())

(GAP) Flat(List([0..11], n->List([0..n], k->(n+1-k)*(4*k+1)))); # Muniru A Asiru, Mar 07 2019

(Magma) [[(n+1-k)*(4*k+1): k in [0..n]]: n in [0..10]]; // G. C. Greubel, Mar 07 2019

(Sage) [[(n-k+1)*(4*k+1) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Mar 07 2019

CROSSREFS

Row sums give hexagonal pyramidal numbers A002412.

Cf. A101493 for product B*A, A002412.

Sequence in context: A163254 A277696 A143121 * A297442 A277709 A138765

Adjacent sequences: A101489 A101490 A101491 * A101493 A101494 A101495

KEYWORD

nonn,tabl

AUTHOR

Lambert Klasen (lambert.klasen(AT)gmx.de) and Gary W. Adamson, Jan 21 2005

STATUS

approved

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Last modified December 8 08:56 EST 2022. Contains 358693 sequences. (Running on oeis4.)