0,3

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 06 2008: (Start)

Equals right border of triangle A143970.

Starting (1, 11, 31, 161,...) = row sums of triangle A143970 and INVERT transform of (1, 10, 10, 10,...). (End)

Binomial transform of [1, 0, 10, 0, 100, 0, 1000, 0, 10000, 0, ...]=: powers of 10 (A011557) with interpolated zeros . Inverse binomial transform of A084132 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 02 2008]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

A. Tarn, Approximations to certain square roots and the series of numbers connected therewith, Mathematical Questions and Solutions from the Educational Times, 1 (1916), 8-12.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

a(n)=(1+sqrt(10))^n/2+(1-sqrt(10))^n/2; G.f.: (1-x)/(1-2x-9x^2); E.g.f.: exp(x)cosh(sqrt(10)x). - Paul Barry (pbarry(AT)wit.ie), May 16 2003

a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*10^(n-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 26 2007

A002535:=(-1+z)/(-1+2*z+9*z**2); [Conjectured by S. Plouffe in his 1992 dissertation.]

A143970 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 06 2008]

Sequence in context: A094622 A001604 A144727 this_sequence A128337 A093382 A098264

Adjacent sequences: A002532 A002533 A002534 this_sequence A002536 A002537 A002538

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).