A140978 - OEIS

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A140978

Repeat (n+1)^2 n times.

4, 9, 9, 16, 16, 16, 25, 25, 25, 25, 36, 36, 36, 36, 36, 49, 49, 49, 49, 49, 49, 64, 64, 64, 64, 64, 64, 64, 81, 81, 81, 81, 81, 81, 81, 81, 100, 100, 100, 100, 100, 100, 100, 100, 100, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

See A093995.

Frenicle writes the entries in the form a(n) = A055096(n)-A133819(n), with the flattened index view of A133819: 4=5-1, 9=10-1, 9=13-4, 16=17-1, 16=20-4, 16=25-9 etc.

Also triangle T(n, k) = (n+1)^2, 1<=k<=n. - Michel Marcus, Feb 03 2013

LINKS

Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened

M. de Frenicle, Methode pour trouver la solutions des problemes par les exclusions, in: Divers ouvrages des mathematiques et de physique par messieurs de l'academie royale des sciences, (1693) pp 1-44, table page 11.

FORMULA

a(n)=(A003057(n+1))^2. - R. J. Mathar, Aug 25 2008

MATHEMATICA

Table[PadRight[{}, n, (n+1)^2], {n, 10}]//Flatten (* Harvey P. Dale, Oct 10 2019 *)

PROG

(Haskell)

a140978 n k = a140978_tabl !! (n-1) !! (k-1)

a140978_row n = a140978_tabl !! (n-1)

a140978_tabl = map snd $ iterate

(\(i, xs@(x:_)) -> (i + 2, map (+ i) (x:xs))) (5, [4])

-- Reinhard Zumkeller, Mar 23 2013

(Python)