A036449 Values square, differences triangular.

0, 1, 4, 25, 196, 1681, 2116, 18769, 168100, 1510441, 13586596, 14577124, 15856324, 16120225, 16289296, 16736281, 150601984, 151782400, 1365967681, 1368334081, 1393379584, 1640655025, 1649578225, 1669212736, 1725737764

Offset

1,3

Links

Donovan Johnson, Table of n, a(n) for n = 1..145

Mathematica

triangularQ[n_] := IntegerQ[Sqrt[8n + 1]]; a[1] = 0; a[n_] := a[n] = (b = Sqrt[a[n-1]]; While[b++; ! triangularQ[b^2 - a[n-1]]]; b^2); Table[a[n], {n, 1, 25}] (* Jean-François Alcover, Oct 04 2011 *)

Prog

(Haskell)
a036449 n = a036449_list !! (n-1)
a036449_list = map fst listsOfValsAndDiffs
a189475 n = a189475_list !! (n-1)
a189475_list = tail $ map snd listsOfValsAndDiffs
listsOfValsAndDiffs = (0, 1) : f (0, 1) where
   f (x, y) = (u, v) : f (u, v) where
     u = x + v
     v = head $ dropWhile ((== 0) . a010052 . (+ x)) $ tail a000217_list
-- Reinhard Zumkeller, Apr 23 2011
(Python)
from itertools import count, islice
from sympy import integer_nthroot
def A036449_gen(): # generator of terms
    yield (a:=0)
    for n in count(1):
        if integer_nthroot(((b:=n**2)-a<<3)+1, 2)[1]:
            yield (a:=b)
A036449_list = list(islice(A036449_gen(), 20)) # Chai Wah Wu, Nov 14 2022

Crossrefs

Cf. A000217, A010052, A000290, A010054, A189475 (first differences).

Sequence in context: A171791 A060908 A322442 * A051500 A206179 A151342

Adjacent sequences: A036446 A036447 A036448 * A036450 A036451 A036452

Keyword

nonn,nice

Author

David W. Wilson

Extensions

Offset corrected by Donovan Johnson, Jan 20 2011

Status

approved