

A076921


Smallest number such that the highest common factor of pair of successive terms follows the pattern 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, ..., i.e., b(2n1) = b(2n) = n given by A004526.


1



1, 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, 49, 56, 64, 72, 81, 90, 100, 110, 121, 132, 144, 156, 169, 182, 196, 210, 225, 240, 256, 272, 289, 306, 324, 342, 361, 380, 400, 420, 441, 462, 484, 506, 529, 552, 576, 600, 625, 650, 676, 702, 729, 756, 784
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OFFSET

1,3


COMMENTS

(1) a(2n) = n^2, a(2n1) = n(n+1) = twice the nth triangular number. (2) Geometric mean of the successive squares interleaved between them.
Essentially the same as A002620.


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (2,0,2,1).


FORMULA

Empirical: a(n+1) + a(n) = binomial(n+1,2), a(1) = a(2) = 1.  G. C. Greubel, Oct 29 2017


MATHEMATICA

Join[{1}, LinearRecurrence[{2, 0, 2, 1}, {1, 2, 4, 6}, 50]] (* G. C. Greubel, Oct 29 2017 *)


CROSSREFS

Cf. A004526.
Sequence in context: A086378 A088900 A083392 * A002620 A087811 A025699
Adjacent sequences: A076918 A076919 A076920 * A076922 A076923 A076924


KEYWORD

nonn,easy


AUTHOR

Amarnath Murthy, Oct 17 2002


EXTENSIONS

More terms from Philippe Deléham, Jun 20 2005


STATUS

approved



