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A055461 Square decrescendo subsequences: triangle T(n,k) = (n-k)^2, n >= 1, 0 <= k < n. 5
1, 4, 1, 9, 4, 1, 16, 9, 4, 1, 25, 16, 9, 4, 1, 36, 25, 16, 9, 4, 1, 49, 36, 25, 16, 9, 4, 1, 64, 49, 36, 25, 16, 9, 4, 1, 81, 64, 49, 36, 25, 16, 9, 4, 1, 100, 81, 64, 49, 36, 25, 16, 9, 4, 1, 121, 100, 81, 64, 49, 36, 25, 16, 9, 4, 1, 144, 121, 100, 81, 64, 49, 36, 25, 16, 9, 4, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums are A000330. - Michel Marcus, Dec 31 2012

Alternating row sums are A000217. - Omar E. Pol, Jan 24 2014

LINKS

Robert Israel, Table of n, a(n) for n = 1..10011 (rows 1 to 141, flattened)

FORMULA

a(n) = A004736(n)^2

G.f. as triangle: x*(1+x)/((1-x*y)*(1-x)^3). - Robert Israel, Jan 18 2018

EXAMPLE

1; 4 1; 9 4 1; 16 9 4 1; etc.

From Omar E. Pol, Jan 26 2014: (Start)

Triangle begins:

1;

4,    1;

9,    4,  1;

16,   9,  4,  1;

25,  16,  9,  4,  1;

36,  25, 16,  9,  4,  1;

49,  36, 25, 16,  9,  4,  1;

64,  49, 36, 25, 16,  9,  4,  1;

81,  64, 49, 36, 25, 16,  9,  4,  1;

100, 81, 64, 49, 36, 25, 16,  9,  4,  1;

...

For n = 7 the row sum is 49 + 36 + 25 + 16 + 9 + 4 + 1 = A000330(7) = 140. The alternating row sum is 49 - 36 + 25 - 16 + 9 - 4 + 1 = A000217(7) = 28.

(End)

MAPLE

for n from 1 to 10 do

  seq((n-k)^2, k=0..n-1)

od; # Robert Israel, Jan 18 2018

CROSSREFS

Sequence in context: A261981 A153265 A085691 * A104796 A132020 A175643

Adjacent sequences:  A055458 A055459 A055460 * A055462 A055463 A055464

KEYWORD

easy,nonn,tabl

AUTHOR

Henry Bottomley, Jun 26 2000

STATUS

approved

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Last modified October 23 03:21 EDT 2018. Contains 316519 sequences. (Running on oeis4.)