This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A099429 #25 Sep 08 2022 08:45:15
%S A099429 0,0,2,3,12,25,66,147,344,765,1710,3751,8196,17745,38234,81915,174768,
%T A099429 371365,786438,1660239,3495260,7340025,15379122,32156323,67108872,
%U A099429 139810125,290805086,603979767,1252698804,2594876065,5368709130,11095332171,22906492256
%N A099429 A Jacobsthal-Lucas convolution.
%C A099429 Inverse binomial transform is (-1)^n * a(n). - _Michael Somos_, Jun 02 2014
%C A099429 If we concatenate the lexicographically ordered bit strings of length n, then a(n) is the number of times 11 appears as a substring, if overlapping substrings are not considered as being separate. - _John M. Campbell_, Jan 18 2019
%H A099429 G. C. Greubel, <a href="/A099429/b099429.txt">Table of n, a(n) for n = 0..1000</a>
%H A099429 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-4,-4).
%F A099429 G.f.: x^2*(2-x)/(1-x-2*x^2)^2. [Typo corrected by _Colin Barker_, Jun 16 2012]
%F A099429 a(n) = Sum_{k=0..n} J(n-k)*(2^(k-1) -(-1)^k +0^k/2).
%F A099429 a(n) = Sum_{k=0..n+1} J(n-k)*binomial(n-k+1, k)*binomial(1, (k+1)/2)*(1-(-1)^k)/2.
%F A099429 a(n) = A036289(n)/6 +(-1)^n*n/3. - _R. J. Mathar_, Sep 21 2012
%F A099429 a(-n) = (-2)^(-n-1) * A193449(n) for all n in Z. - _Michael Somos_, Jun 02 2014
%e A099429 G.f. = 2*x^2 + 3*x^3 + 12*x^4 + 25*x^5 + 66*x^6 + 147*x^7 + 344*x^8 + ...
%e A099429 If we concatenate the lexicographically ordered bit strings of length 4, we obtain the expression 0000000100100011010001010110011110001001101010111100110111101111, and we see that the substring 11 appears a total of a(4) = 12 times, with overlapping substrings not being considered as being separate. - _John M. Campbell_, Jan 18 2019
%t A099429 CoefficientList[Series[x^2*(2-x)/(1-x-2x^2)^2, {x, 0, 32}], x] (* _Michael De Vlieger_, Jan 18 2019 *)
%o A099429 (PARI) {a(n) = if( n>=0, polcoeff( x^2*(2-x)/((1+x)*(1-2*x))^2 + x*O(x^n), n), polcoeff( x*(1-2*x)/((1+x)*(2-x))^2 + x*O(x^-n), -n) )}; /* _Michael Somos_, Jun 02 2014 */
%o A099429 (Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); [0,0] cat Coefficients(R!( x^2*(2-x)/(1-x-2*x^2)^2 )); // _G. C. Greubel_, Feb 25 2019
%o A099429 (Sage) (x^2*(2-x)/(1-x-2*x^2)^2).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Feb 25 2019
%Y A099429 Cf. A001045, A014551, A193449.
%K A099429 easy,nonn
%O A099429 0,3
%A A099429 _Paul Barry_, Oct 15 2004