A189475 First differences of A036449, triangular numbers by definition.

1, 3, 21, 171, 1485, 435, 16653, 149331, 1342341, 12076155, 990528, 1279200, 263901, 169071, 446985, 133865703, 1180416, 1214185281, 2366400, 25045503, 247275441, 8923200, 19634511, 56525028, 229847520, 739374285, 224497455, 81939201, 24010841091, 1106357280

Offset

1,2

Links

Donovan Johnson, Table of n, a(n) for n = 1..144

Formula

a(n) = A036449(n+1) - A036449(n). [Corrected by Georg Fischer, Dec 11 2022]

A010054(a(n)) = 1.

Prog

(Haskell) Cf. program in A036449 (simultaneous computation).
(Python)
from itertools import count, islice
from sympy import integer_nthroot
def A189475_gen(): # generator of terms
    a = 0
    for n in count(1):
        if integer_nthroot(((b:=n**2)-a<<3)+1, 2)[1]:
            yield b-a
            a = b
A189475_list = list(islice(A189475_gen(), 20)) # Chai Wah Wu, Nov 14 2022

Crossrefs

Cf. A010054, A036449.

Subsequence of A000217.

Sequence in context: A220103 A132805 A372459 * A331328 A372089 A206178

Adjacent sequences: A189472 A189473 A189474 * A189476 A189477 A189478

Keyword

nonn

Author

Reinhard Zumkeller, Apr 23 2011

Status

approved